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51×5152×5253×5354×5455×5556×56=2601=2704=2809=2916=3025=3136⋮
What is the value of 57×57?
Bonus: Can you explain why this pattern appears, and when it breaks?
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In the diagram, the yellow and red circles are identical and are both centered on the larger circle's diameter.
Which has a larger area?
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In a 90-question, multiple-choice test, a student gets
If the student attempted every single question, can he or she get a total score of exactly 300?
For example, if the student only got 60 correct answers (30 incorrect), then the total score would be 60×4−30×1=210.
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What mass (in kilograms) on the left side would keep the system in balance?
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We have two copper spheres of the same radius; one is hollow (vacuum inside) and the other is solid. Initially, both spheres are in a vacuum at the same temperature. Then they are heated up to the same temperature which causes them both to expand.
Which sphere has the greater final radius?
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